The part of a word that is only sometimes a free morpheme is the root word.
A root word may stand alone as a free morpheme (like "book"), but it can also be bound when combined with prefixes and suffixes to form new words (like "unhappiness," where "happy" is the root but "un-" and "-ness" are bound morphemes). The base word, however, is often considered a full free morpheme since it can often stand alone. Prefixes and suffixes are typically bound morphemes and cannot stand alone.